Question

(x − 6)2 − 10 = −7 solve using the square root property

Answer 1

Answer:

x1 = +√3 + 6

x2 = -√3 + 6

Step-by-step explanation:

To solve this equation, using the square root property, you need to understand first this property before you try to solve the value of x

This method is generally used on equations that have the form

ax2 = c   or   (ax + b)2 = c, This last one is our case.    

Now, to solve the equation, you need to isolate the term that contains the squared variable. You can then take the square root of both sides and solve for the variable.  

You shouldn Note that there is always the possibility of two roots for every square root: one positive and one negative. In these cases, you should  Place a  ± sign in front of the side containing the constant after you take the square root, and this, will ensure that the final answer will include both possible roots.

Now that we know the property, let's see how to solve this problem:

(x - 6)^2 - 10 = -7

Let's pass the -10 to the right side

(x - 6)^2 = -7 + 10

(x - 6)^2 = 3

Now we have an expression that looks like (ax + b)^2 = c, so, let's take the square root both sides of the equation:

√(x - 6)^2 = √3

x - 6 = √3

x = ±√3 + 6

Finally, as I stated before, we should put the + and - signs because we have two possibilities, so the two possible values for x would be:

x1 = +√3 + 6

x2 = -√3 + 6